Many applied techniques involve detection of pulses. Such techniques are applied in such fields as geology (e.g., for exploration for deposits of oil, gas, or other underground resources), detection (e.g., radar, lidar, and sonar), and communication. In these fields, a pulse (e.g., acoustic or electromagnetic) is created at one location for detection at another location, or for detection after reflection at the same location. In other fields, pulses that are remotely created by natural or manmade processes are detected and interpreted.
A pulse may be defined by its intensity as a function of time. A transmitted pulse may be characterized by a high intensity (e.g., relative to random background intensity fluctuations) as a function of time. A short pulse may be decomposed (e.g., by Fourier analysis or similar techniques) into a series of continuous waves of different frequency. Each component wave is characterized by an amplitude and phase.
In some cases, the pulse may pass through a dispersive medium through which waves of different frequency travel at different speeds. As a result of traversing the dispersive medium, the arrival times at the detector of different frequency components of the pulse may differ from one another. Equivalently, the phases of the component waves may be shifted by the traversal of the dispersive medium. As a result of travel through the dispersive medium, the pulse may become degraded (e.g., be transformed into a longer pulse with reduced intensity). In some cases, the dispersion may cause the pulse to become indistinguishable from random intensity fluctuations of the received signal.
Thus, it may become difficult to detect or interpret a pulse that has traversed a dispersive medium.